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When there appears the relative motion between the sound source and the receiver, the received tonal signal will produce Doppler shift, and the Doppler information is relevant to the motion parameters of the target. According to the acoustic Doppler shift frequency, we propose the Doppler-warping transformation. The phase linearization of the Doppler signal can be realized by using the transformation. Then, we deduce the warping operator and propose an algorithm for estimating the target motion parameters by using the proposed transformation. Firstly, the Doppler-warping operator under different motion parameters is constructed. Secondly, the time resampling of the received time-domain signal is performed by using the operator. Then, the spectral function of the transformed signal is calculated. Finally, the spectral function entropy is minimized to estimate the objective parameter. The simulation results show the effectiveness of the proposed method. For a low signal-to-noise ratio of sea trial data, where the real speed of a fishing boat is 4.5 m/s, the result from the traditional minimum mean square error (MMSE) velocity estimation method is 5.2 m/s, and the estimation error is 15.56%. The proposed Doppler-warping transform method can estimate the target velocity more accurately, specifically, it is 4.7 m/s and its corresponding estimation error is 4.44%.
[1] 汪德昭, 尚尔昌 2013 水声学(第二版) (北京: 科学出版社) 第345−347页
Wang D Z, Shang E C 2013 Underwater Acoustics (Vol. 2) (Beijing: Science Press) pp345−347 (in Chinese)
[2] 吴国清, 李靖, 陈耀明, 袁毅 1999 声学学报 24 6
Google Scholar
Wu G Q, Li J, Chen Y M, Yuan Y 1999 Acta Acustica 24 6
Google Scholar
[3] 杨德森, 吴一 1996 哈尔滨工程大学学报 17 38
Yang D S, Wu Y 1996 J. Harbin Engineering Univ. 17 38
[4] Ferguson B G, Quinn B G 1994 J. Acoust. Soc. Am. 96 821
Google Scholar
[5] Reid D C, Zoubir A M, Boashash B 1997 J. Acoust. Soc. Am. 102 207
Google Scholar
[6] Valiere J C, Poisson F, Depollier C, Simon L 1999 IEEE Signal Process Lett. 6 113
Google Scholar
[7] Xu L J, Yang Y X, Yu S D 2015 J. Acoust. Soc. Am. 137 320
Google Scholar
[8] Liang N N, Yang Y X, Guo X J 2019 J. Acoust. Soc. Am. 145 34
Google Scholar
[9] Quinn B G 1998 J. Acoust. Soc. Am. 98 2560
[10] 邹红星, 周小波, 李衍达 2000 清华大学学报(自然科学版) 40 55
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Zou H X, Zhou X B, Li Y D 2000 J. Tsinghua Univ. (Sci. & Tech.) 40 55
Google Scholar
[11] 吴国清, 陈永强 2003 声学学报 28 130
Google Scholar
Wu G Q, Chen Y Q 2003 Acta Acustica 28 130
Google Scholar
[12] Timlelt H, Remram Y, Belouchrani A 2017 Digital Signal Processing 63 35
Google Scholar
[13] 刘凯悦, 彭朝晖, 张灵珊, 王光旭 2020 应用声学 39 236
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Liu K Y, Peng Z H, Zhang L S, Wang G X 2020 Appl. Acoust. 39 236
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[14] Baraniuk R G, Jones D L 1995 IEEE Trans. Signal Process. 43 2269
Google Scholar
[15] Bonnel J, Thode A, Wright D, Chapman R 2020 J. Acoust. Soc. Am. 147 1897
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[16] Le Touze G, Torras J, Nicolas B, Mars J 2008 IEEE Oceans 2008 Quebec City, Canada, September 15–18, 2008 p1
[17] 戚聿波, 周士弘, 张仁和, 张波, 任云 2014 物理学报 63 044303
Google Scholar
Qi Y B, Zhou S H, Zhang R H, Zhang B, Ren Y 2014 Acta Phys. Sin. 63 044303
Google Scholar
[18] Bonnel J, Dosso S, Chapman R 2013 J. Acoust. Soc. Am. 134 120
Google Scholar
[19] Li F H, Zhang B, Guo Y G 2014 Chin. Phys. Lett. 31 024301
Google Scholar
[20] Niu H Q, Zhang R H, Li Z L, Guo Y G, He L 2013 Chin. Phys. Lett. 30 84301
Google Scholar
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图 1 声源运动接收器静止示意图
Figure 1. Moving sound source and stationary receiver.
图 2 (a)多普勒信号时频图; (b)瞬时频率真实值和估计值; (c)最小均方误差估计的速度值和真实值对比
Figure 2. (a) Time-frequency distribution of Doppler signal; (b) real and estimated instantaneous frequency; (c) comparison of real velocity and estimation velocity obtained by MMSE.
图 3 (a)不同速度值下Doppler-warping变换后的信号频谱; (b) Doppler-warping变换估计速度的结果
Figure 3. (a) Signal spectra after the Doppler-warping transform under different velocity values; (b) result of velocity estimation by the Doppler-warping transform.
图 4 不同信噪比下估计的速度结果
Figure 4. Estimated velocity results under different SNRs.
图 5 SNR = –10 dB时的(a)时频分布图, (b)瞬时频率真实值和估计值, 以及(c) v = 5 m/s 条件下Doppler-warping变换后的频谱和原始信号频谱的对比
Figure 5. (a) Time-frequency distribution; (b) real and estimated instantaneous frequency; (c) comparison of signal spectrum after the Doppler-warping transform with v = 5 m/s and the spectrum of the original signal. SNR = –10 dB.
图 6 (a)目标船运动轨迹; (b)水体声速剖面
Figure 6. (a) Track of the target ship; (b) sound speed profile.
图 7 海试数据分析 (a)时频图; (b)瞬时频率理论值和估计值; (c) MMSE计速度的结果; (d) Doppler-warping变换估计速度的结果
Figure 7. Analysis of the sea trial data: (a) Time-frequency distribution; (b) theoretical and estimated instantaneous frequency; (c) result of velocity estimation by MMSE; (d) result of velocity estimation by the Doppler-warping transform.
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[1] 汪德昭, 尚尔昌 2013 水声学(第二版) (北京: 科学出版社) 第345−347页
Wang D Z, Shang E C 2013 Underwater Acoustics (Vol. 2) (Beijing: Science Press) pp345−347 (in Chinese)
[2] 吴国清, 李靖, 陈耀明, 袁毅 1999 声学学报 24 6
Google Scholar
Wu G Q, Li J, Chen Y M, Yuan Y 1999 Acta Acustica 24 6
Google Scholar
[3] 杨德森, 吴一 1996 哈尔滨工程大学学报 17 38
Yang D S, Wu Y 1996 J. Harbin Engineering Univ. 17 38
[4] Ferguson B G, Quinn B G 1994 J. Acoust. Soc. Am. 96 821
Google Scholar
[5] Reid D C, Zoubir A M, Boashash B 1997 J. Acoust. Soc. Am. 102 207
Google Scholar
[6] Valiere J C, Poisson F, Depollier C, Simon L 1999 IEEE Signal Process Lett. 6 113
Google Scholar
[7] Xu L J, Yang Y X, Yu S D 2015 J. Acoust. Soc. Am. 137 320
Google Scholar
[8] Liang N N, Yang Y X, Guo X J 2019 J. Acoust. Soc. Am. 145 34
Google Scholar
[9] Quinn B G 1998 J. Acoust. Soc. Am. 98 2560
[10] 邹红星, 周小波, 李衍达 2000 清华大学学报(自然科学版) 40 55
Google Scholar
Zou H X, Zhou X B, Li Y D 2000 J. Tsinghua Univ. (Sci. & Tech.) 40 55
Google Scholar
[11] 吴国清, 陈永强 2003 声学学报 28 130
Google Scholar
Wu G Q, Chen Y Q 2003 Acta Acustica 28 130
Google Scholar
[12] Timlelt H, Remram Y, Belouchrani A 2017 Digital Signal Processing 63 35
Google Scholar
[13] 刘凯悦, 彭朝晖, 张灵珊, 王光旭 2020 应用声学 39 236
Google Scholar
Liu K Y, Peng Z H, Zhang L S, Wang G X 2020 Appl. Acoust. 39 236
Google Scholar
[14] Baraniuk R G, Jones D L 1995 IEEE Trans. Signal Process. 43 2269
Google Scholar
[15] Bonnel J, Thode A, Wright D, Chapman R 2020 J. Acoust. Soc. Am. 147 1897
Google Scholar
[16] Le Touze G, Torras J, Nicolas B, Mars J 2008 IEEE Oceans 2008 Quebec City, Canada, September 15–18, 2008 p1
[17] 戚聿波, 周士弘, 张仁和, 张波, 任云 2014 物理学报 63 044303
Google Scholar
Qi Y B, Zhou S H, Zhang R H, Zhang B, Ren Y 2014 Acta Phys. Sin. 63 044303
Google Scholar
[18] Bonnel J, Dosso S, Chapman R 2013 J. Acoust. Soc. Am. 134 120
Google Scholar
[19] Li F H, Zhang B, Guo Y G 2014 Chin. Phys. Lett. 31 024301
Google Scholar
[20] Niu H Q, Zhang R H, Li Z L, Guo Y G, He L 2013 Chin. Phys. Lett. 30 84301
Google Scholar
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